You can use the tags [quote=]quoted post[/quote] to quote somebody's post.
A little explanation:
The technique is called "power stealing". It's used in thermostats because older ones didn't have a common wire. Their suggested (no doorbell) and resistor, means the Ring doorbell sees a current limited by 25 ohms supply when the button is NOT PRESSED. It has to have it's own power for the duration of the press. One method is a "supercap" or a big capacitor.
16 VAC is not a common relay coil value. It is for a doorbell. It's good that the ring doorbell operates to 24 V. You almost never get 24 VAC from a 24 VAC transformer. It's usually higher. Not sure what the resistance of a typical door chime is. But, it's the combination of that coil resistance that keeps things happy. It must be low enough, but not less than about 25 ohms. It must be high enough,, so the Ring doorbell can "charge" as you put it.
I want to bring up a 12 VDC to 24 VAC inverter.
https://www.powerstream.com/inv-12dc-24vac.htm This is the only one I know of. It's likely not appropriate for anything..
You can probably get the desired effect with this
https://interfacesolutions.uk.com/product/ac-dc-relay/ from the UK.
You can test, by hooking the Ring doorbell up using the 25 ohm resistor and the conventional doorbell power supply. Put a 360 ohm resistor across the back terminals.
measure the voltage when the doorbell is not pressed and when the doorbell is pressed and see about how long the activation lasts. If that test gives me the right numbers, the system should work.
The voltage across the 25 ohm resistor would be useful too pressed and unpressed. The Ring doorbell MAY already limit the amount of on time. This can change the design of the timer related stuff.
If would give you a contact closure that needs to switch 10 mA (typical) to "clean the contacts"
The general problem with the proposed idea, is that it draws a few mA all the time.
This gets you a contact that can't switch the horn directly.
16 VAC coils on relays are hard to come by. Detecting 16 VAC is less difficult.
In the long run, the car battery should probably go. An option is here:
https://www.powerstream.com/low-noise-high-power.htm Measuring the horn current could help select this too.
In any event, the automotive relay
**broken link removed** has been tried and true for driving the horn. Sockets are available too.